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The article demonstrates rather general approach to problems of discrete geometry: treat them as global optimization problems to be solved by one of general purpose solver implementing branch-and-bound algorithm (B&B). This approach may be…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…
The thermal unit commitment (UC) problem often can be formulated as a mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. In this paper, with projecting unit generation…
Mixed-Integer Quadratic Programming (MIQP) has been identified as a suitable approach for finding an optimal solution to the behavior planning problem with low runtimes. Logical constraints and continuous equations are optimized alongside.…
A control optimization approach is presented for a chaser spacecraft tasked with maintaining proximity to a target space object while avoiding collisions. The target object trajectory is provided numerically to account for both passive…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of…
We consider the central role of improving directions in solution methods for mixed integer bilevel linear optimization problems (MIBLPs). Current state-of-the-art methods for solving MIBLPs employ the branch-and-cut framework originally…
In this work, we introduce and study the $p$-$\alpha$-closest-center problem ($p\alpha$CCP), which generalizes the $p$-second-center problem, a recently emerged variant of the classical $p$-center problem. In the $p\alpha$CCP, we are given…
Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
In this paper, we address a variant of the marketing mix optimization (MMO) problem which is commonly encountered in many industries, e.g., retail and consumer packaged goods (CPG) industries. This problem requires the spend for each…
For sufficiently large $n$, we show that in every configuration of $n$ points chosen inside the unit square there exists a triangle of area less than $n^{-8/7-1/2000}$. This improves upon a result of Koml\'os, Pintz and Szemer\'edi from…
According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive and negative edges are respectively located inside and between the…
Mixed Hamming packings are considered: the maximal cardinality given a minimum codeword Hamming distance of mixed codes is addressed via mixed integer programming models. Adopting the concept of contact graph from classical continuous…
In this paper, we describe the first mixed-integer nonlinear programming (MINLP) based solution approach that successfully identifies the most energy-efficient distillation configuration sequence for a given separation. Current sequence…
The state-of-the-art in optimal control from timed temporal logic specifications, including Metric Temporal Logic (MTL) and Signal Temporal Logic (STL), is based on Mixed-Integer Convex Programming (MICP). The standard MICP approach is…
We present an exact formulation of the symmetric Traveling Salesman Problem (TSP) that replaces the classical edge-selection view with a surface-building approach. Instead of selecting edges to form a cycle, the model selects a set of…
Perfectly matched layers (PMLs) are formulated and applied to numerically solve nonlocal Helmholtz equations in one and two dimensions. In one dimension, we present the PML modifications for the nonlocal Helmholtz equation with general…